Search for a Lorentz invariance violation in atmospheric neutrino oscillations using MACRO data

The energy spectrum of neutrino-induced upward-going muons in MACRO was analysed in terms of special relativity principles violating effects, keeping standard mass-induced atmospheric neutrino oscillations as the dominant source of nu_mu nu_tau transitions. The data disfavour these exotic possibilities even at a sub-dominant level, and stringent 90% C.L. limits are placed on the Lorentz invariance violation parameters. These limits can also be re-interpreted as upper bounds on the parameters describing violation of the Equivalence Principle.Comment: 8 pages, 5 EPS figures, uses article.sty. Invited talk at C2CR 2005, From Colliders to Cosmic Rays, Prague, Czech Republic, 7-13 September 200

Diffraction Resistant Scalar Beams Generated by a Parabolic Reflector and a Source of Spherical Waves

In this work, we propose the generation of diffraction resistant beams by using a parabolic reflector and a source of spherical waves positioned at a point slightly displaced from its focus (away from the reflector). In our analysis, considering the reflector dimensions much greater than the wavelength, we describe the main characteristics of the resulting beams, showing their properties of resistance to the diffraction effects. Due to its simplicity, this method may be an interesting alternative for the generation of long range diffraction resistant waves.Comment: 22 pages, 9 figures, Applied Optics, 201

A new multiparametric topological method for determining the primary cosmic ray mass composition in the knee energy region

The determination of the primary cosmic ray mass composition from the characteristics of extensive air showers (EAS), obtained at an observation level in the lower half of the atmosphere, is still an open problem. In this work we propose a new method of the Multiparametric Topological Analysis and show its applicability for the determination of the mass composition of the primary cosmic rays at the PeV energy region.Comment: 8 pages, 4 figures, talk given at Vulcano 2004 Workshop 'Frontier Objects in Physics and Astrophysics', Vulcano, Italy, 24-29.05.04, to be published in the Proceedings of the Worksho

Damage as Gamma-limit of microfractures in anti-plane linearized elasticity

A homogenization result is given for a material having brittle inclusions arranged in a periodic structure. <br/> According to the relation between the softness parameter and the size of the microstructure, three different limit models are deduced via Gamma-convergence. <br/> In particular, damage is obtained as limit of periodically distributed microfractures

On the dynamics of WKB wave functions whose phase are weak KAM solutions of H-J equation

In the framework of toroidal Pseudodifferential operators on the flat torus $\Bbb T^n := (\Bbb R / 2\pi \Bbb Z)^n$ we begin by proving the closure under composition for the class of Weyl operators $\mathrm{Op}^w_\hbar(b)$ with simbols $b \in S^m (\mathbb{T}^n \times \mathbb{R}^n)$. Subsequently, we consider $\mathrm{Op}^w_\hbar(H)$ when $H=\frac{1}{2} |\eta|^2 + V(x)$ where $V \in C^\infty (\Bbb T^n;\Bbb R)$ and we exhibit the toroidal version of the equation for the Wigner transform of the solution of the Schr\"odinger equation. Moreover, we prove the convergence (in a weak sense) of the Wigner transform of the solution of the Schr\"odinger equation to the solution of the Liouville equation on $\Bbb T^n \times \Bbb R^n$ written in the measure sense. These results are applied to the study of some WKB type wave functions in the Sobolev space $H^{1} (\mathbb{T}^n; \Bbb C)$ with phase functions in the class of Lipschitz continuous weak KAM solutions (of positive and negative type) of the Hamilton-Jacobi equation $\frac{1}{2} |P+ \nabla_x v_\pm (P,x)|^2 + V(x) = \bar{H}(P)$ for $P \in \ell \Bbb Z^n$ with $\ell >0$, and to the study of the backward and forward time propagation of the related Wigner measures supported on the graph of $P+ \nabla_x v_\pm$

Precise determination of muon and electromagnetic shower contents from shower universality property

We consider two new aspects of Extensive Air Shower development universality allowing to make accurate estimation of muon and electromagnetic (EM) shower contents in two independent ways. In the first case, to get muon (or EM) signal in water Cherenkov tanks or in scintillator detectors it is enough to know the vertical depth of shower maximum and the total signal in the ground detector. In the second case, the EM signal can be calculated from the primary particle energy and the zenith angle. In both cases the parametrizations of muon and EM signals are almost independent on primary particle nature, energy and zenith angle. Implications of the considered properties for mass composition and hadronic interaction studies are briefly discussed. The present study is performed on 28000 of proton, oxygen and iron showers, generated with CORSIKA 6.735 for $E^{-1}$ spectrum in the energy range log(E/eV)=18.5-20.0 and uniformly distributed in cos^2(theta) in zenith angle interval theta=0-65 degrees for QGSJET II/Fluka interaction models.Comment: Submitted to Phys. Rev.

Fokker-Planck type equations with Sobolev diffusion coefficients and BV drift coefficients

In this paper we give an affirmative answer to an open question mentioned in [Le Bris and Lions, Comm. Partial Differential Equations 33 (2008), 1272--1317], that is, we prove the well-posedness of the Fokker-Planck type equations with Sobolev diffusion coefficients and BV drift coefficients.Comment: 11 pages. The proof has been modifie